Question: Solve for $x$ and $y$ using elimination. ${-6x+3y = 15}$ ${-5x+5y = 30}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-5$ and the bottom equation by $3$ ${30x-15y = -75}$ $-15x+15y = 90$ Add the top and bottom equations together. $15x = 15$ $\dfrac{15x}{{15}} = \dfrac{15}{{15}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-6x+3y = 15}\thinspace$ to find $y$ ${-6}{(1)}{ + 3y = 15}$ $-6+3y = 15$ $-6{+6} + 3y = 15{+6}$ $3y = 21$ $\dfrac{3y}{{3}} = \dfrac{21}{{3}}$ ${y = 7}$ You can also plug ${x = 1}$ into $\thinspace {-5x+5y = 30}\thinspace$ and get the same answer for $y$ : ${-5}{(1)}{ + 5y = 30}$ ${y = 7}$